Talk:Transfinite Induction/Schema 1

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What exactly is the convention regarding precedence of quantifiers and implications? This article previously was (for me, at least) rather hard to sort out, so I parenthesized everything, but is there a convention as to whether

$\forall x : a \implies b$


$\left({\forall x : a}\right) \implies b$


$\forall x : \left({a \implies b}\right)$? --Dfeuer (talk) 00:03, 23 December 2012 (UTC)
I'd be inclined to make quantifiers lowest precedence (i.e., the second) but really parentheses should be added. --Lord_Farin (talk) 00:22, 23 December 2012 (UTC)
Most formal-language treatments of predicate logic are fairly rigorous about such things, and the parentheses would be automatically generated so as for this not to be ambiguous. In this case it seems to be the second case that is required. --prime mover (talk) 06:13, 23 December 2012 (UTC)